David Cameron had claimed that 40% of recently arrived EU migrants were dependent on benefits.
Photograph: Andy Rain/EPA

A total of 84,000 EU migrant families on tax credits would have been affected by David Cameron’s “emergency brake” if it had been introduced four years ago, official figures reveal.

The number – released by HMRC six months after it was first requested by the Guardian – appears far smaller than had been suggested by the prime minister in previous public statements justifying the plan.

“The number of EU families that claimed tax credits in 2013/14 and had been issued a NINO [national insurance number] during the previous four years was 84,000,” HMRC said.

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The HMRC disclosure reveals that, if the brake had been introduced four years ago, 84,000 families would have had some or all of their benefits restricted.

The disclosure came as the prime minister lobbied fellow EU leaders on the margins of the Syria conference in London ahead of the European Council later this month. He met Donald Tusk, the European Council president who outlined the plan for the emergency brake in his new settlement for the UK on Tuesday, as well as his counterparts from Slovakia, Greece, Sweden and Belgium.

Lord Rose of Monewden, the former Marks and Spencer boss who chairs the Britain Stronger in Europe campaign, said he was confident the pro-EU side would win the referendum by a “substantial margin”. Rose told a Westminster lunch: “A win’s a win. If we get the 50.001 [%] it is a win – I want to win, but we will win by a substantial margin.”

Anti-EU campaigners are likely to seize on the figures uncovered by the Guardian which show that fewer than expected EU migrants would be affected by the emergency brake. Previously, Cameron had appeared to indicate that many more families would be affected. Speaking in the Commons on Wednesday, he claimed 40% of EU migrants coming to Britain access the in-work benefits system. A briefing from Number 10 and given to the Times [paywall] in November said this amounted to 148,000 people.

A spokesperson for No 10 said on Thursday: “The proposal is designed to address the unnatural draw of our welfare system, which provides an additional incentive for people to move to the UK to work. These figures underline exactly why the proposals on limiting in-work benefits for new EU migrants are vital.

“As the DWP release in November demonstrated, around 40 per cent of EU migrants who have arrived in the last four years are supported by the benefits system. Tax credits are just one part.”

Jonathan Portes, principal research fellow at the National Institute of Economic and Social Research, said: “This new data shows that the prime minister’s claim that 40% of recently arrived European migrants were dependent on benefits was at best selective and misleading.”

Portes said the rate of newly arrived migrants making claims was low and that the overwhelming majority who applied for national insurance numbers were not on benefits.

This showed, he said, that “the prime minister’s focus on this issue is misguided – the emergency brake will have only a modest impact on benefit receipt, and is highly unlikely to have a significant impact on migration flows”.

A second set of figures – also obtained on Thursday four months after they were first requested – show that one in 10 “migrant couples” on tax credits actually include one UK national. HMRC considers a family to be an EU migrant family when at least one member of that family is a migrant from elsewhere in the EU.

Given this broad definition, it remains unclear how many British nationals and their children could be hit by an emergency brake targeted at “migrant families”.

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However, No 10 said this was not the intent. “Our policy is to reduce the pull factor of our welfare system, not to affect British nationals,” a spokesman said.

Downing Street is also facing questions about how its emergency brake on benefits for EU migrants will work, as campaigners on both sides of the referendum debate claimed it would have no impact.

When asked how much the brake would reduce migration, whether it would apply to EU citizens already in the UK, and how it would affect the household claims of British nationals who marry EU migrants, Cameron’s deputy official spokesman acknowledged that many details about the mechanism had yet to be worked out.

“We have a deal on the table and there is clearly some detail still to be filled in, and that is what we are doing over the next couple of weeks,” the No 10 aide said.

The figures were obtained through freedom of information requests to HMRC. The Guardian finally received both sets of information following a complaint to the Information Commissioner’s Office.